Seminars & Events for Ergodic Theory & Statistical Mechanics

October 5, 2017
1:30pm - 3:00pm
Mixing Times for the Ising model
Ergodic Theory & Statistical Mechanics

I will discuss results on the mixing time for the Glauber dynamics for the Ising model and how it relates to the phase transitions of the model.

Speaker: Allan Sly , Princeton University
Location:
Fine Hall 1001
October 12, 2017
1:30pm - 3:00pm
A Lagrangian Fluctuation-Dissipation Relation for Scalar Turbulence
Ergodic Theory & Statistical Mechanics

A common approach to calculate the solution of a scalar advection-diffusion equation is by a Feynman-Kac representation which averages over stochastic Lagrangian trajectories going backward in time to the initial conditions and boundary data. The trajectories are obtained by solving SDE's with the advecting velocity as drift and a backward Itō term representing the scalar diffusivity.  In this framework, we present an exact formula for scalar dissipation in terms of the variance of the scalar values acquired along each random trajectory. As an important application, we study the connection between anomalous scalar dissipation in turbulent flows for large Reynolds and Péclet numbers and the spontaneous stochasticity of the Lagrangian particle trajectories.

Speaker: Theodore Drivas , Princeton University
Location:
Fine Hall 1001
October 19, 2017
1:30pm - 3:00pm
Hadamard well-posedness of the gravity water waves equations
Ergodic Theory & Statistical Mechanics

The gravity water waves equations consist of the incompressible Euler equations and an evolution equation for the free boundary of the fluid domain. Assuming the flow is irrotational, Alazard-Burq-Zuily (Invent. Math, 2014) proved that for any initial data in Sobolev space $H^s$, the problem has a unique solution lying in the same space, here s is the smallest index required to ensure that the fluid velocity is spatially Lipschitz. We will discuss the strategy of a proof of the fact that the flow map is continuous in the strong topology of H^s.

Speaker: Huy Quang Nguyen, Princeton University
Location:
Fine Hall 1001
October 26, 2017
2:00pm - 3:30pm
TBA-: Hahng-Yun Chu
Ergodic Theory & Statistical Mechanics
Speaker: Hahng-Yun Chu, Chungnam National University & Korea Institute for Advanced Study
Location: